Newtons Law of Cooling but for warming??? Please help!

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montalvo.abigail

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When a cold drink is taken from a refrigerator, its temperature is 5 (deg C). After 25 minutes in a 20 (deg C) room its temperature has increased to 10 (deg C).

a) What is the temperature of the drink after 55 minutes?

b) When will its temperature be 17 (deg C)?



I got confused because it's for warming I have no clue on how to even start. Our calculus book didn't cover it and neither did the professor. Please help me out.
 
montalvo.abigail said:
When a cold drink is taken from a refrigerator, its temperature is 5 (deg C). After 25 minutes in a 20 (deg C) room its temperature has increased to 10 (deg C).

a) What is the temperature of the drink after 55 minutes?

b) When will its temperature be 17 (deg C)?



I got confused because it's for warming I have no clue on how to even start. Our calculus book didn't cover it and neither did the professor. Please help me out.
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Why would you even think that was a problem? The situation is "heat transfer". One thing heats up, another cools down. It doesn't matter which direction the heat is going! In fact, if you actually looked at "Newton's law of cooling" it doesn't actually say anything about "cooling". It just says that "heat flows from a warmer body to a cooler body at a rate proportional to the difference in temperature".

So here heat flows from the air to the drink at a rate proportional to the difference in temperature: \(\displaystyle T- T_a\) where T is the temperature of the drink and \(\displaystyle T_a\) is the temperature of the air which, because the air is a very large "heat sink", we can take as a constant. 20 degrees C. If this were a more advanced class you might be expected to solve the differential equation \(\displaystyle \frac{dT}{dt}= k(T- 20)\) but for this class I expect you were given a formula, like \(\displaystyle T= 20+ Ce^{kt}\). That formula has two constants that need to be derminded, C, and k. You are given two "data points", T(0)= 5, T(25)= 15,
to determine C and k.

T(0)= 20+ C= 5 and \(\displaystyle T(25)= 20+ Ce^{25k}= 15\). What are C and k?
 
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